Percolation in random environment

Details Percolation in random environment Percolation in random environment

2002-07-05

arxiv.org/abs/cond-mat/0207157v1

Physical Review E66, 056113 (2002)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 7 figures

Scientific paper

10.1103/PhysRevE.66.056113

We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the system with varying degree of disorder is governed by new, random fixed points with anisotropic scaling properties. For weaker disorder both the magnetization and the anisotropy exponents are non-universal, whereas for strong enough disorder the system scales into an {\it infinite randomness fixed point} in which the critical exponents are exactly known.

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